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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.distribution;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.special.Gamma;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.util.ArithmeticUtils;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.random.RandomGenerator;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.random.Well19937c;<a name="line.26"></a>
<FONT color="green">027</FONT>    <a name="line.27"></a>
<FONT color="green">028</FONT>    /**<a name="line.28"></a>
<FONT color="green">029</FONT>     * Implementation of the Poisson distribution.<a name="line.29"></a>
<FONT color="green">030</FONT>     *<a name="line.30"></a>
<FONT color="green">031</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/Poisson_distribution"&gt;Poisson distribution (Wikipedia)&lt;/a&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * @see &lt;a href="http://mathworld.wolfram.com/PoissonDistribution.html"&gt;Poisson distribution (MathWorld)&lt;/a&gt;<a name="line.32"></a>
<FONT color="green">033</FONT>     * @version $Id: PoissonDistribution.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.33"></a>
<FONT color="green">034</FONT>     */<a name="line.34"></a>
<FONT color="green">035</FONT>    public class PoissonDistribution extends AbstractIntegerDistribution {<a name="line.35"></a>
<FONT color="green">036</FONT>        /**<a name="line.36"></a>
<FONT color="green">037</FONT>         * Default maximum number of iterations for cumulative probability calculations.<a name="line.37"></a>
<FONT color="green">038</FONT>         * @since 2.1<a name="line.38"></a>
<FONT color="green">039</FONT>         */<a name="line.39"></a>
<FONT color="green">040</FONT>        public static final int DEFAULT_MAX_ITERATIONS = 10000000;<a name="line.40"></a>
<FONT color="green">041</FONT>        /**<a name="line.41"></a>
<FONT color="green">042</FONT>         * Default convergence criterion.<a name="line.42"></a>
<FONT color="green">043</FONT>         * @since 2.1<a name="line.43"></a>
<FONT color="green">044</FONT>         */<a name="line.44"></a>
<FONT color="green">045</FONT>        public static final double DEFAULT_EPSILON = 1e-12;<a name="line.45"></a>
<FONT color="green">046</FONT>        /** Serializable version identifier. */<a name="line.46"></a>
<FONT color="green">047</FONT>        private static final long serialVersionUID = -3349935121172596109L;<a name="line.47"></a>
<FONT color="green">048</FONT>        /** Distribution used to compute normal approximation. */<a name="line.48"></a>
<FONT color="green">049</FONT>        private final NormalDistribution normal;<a name="line.49"></a>
<FONT color="green">050</FONT>        /** Distribution needed for the {@link #sample()} method. */<a name="line.50"></a>
<FONT color="green">051</FONT>        private final ExponentialDistribution exponential;<a name="line.51"></a>
<FONT color="green">052</FONT>        /** Mean of the distribution. */<a name="line.52"></a>
<FONT color="green">053</FONT>        private final double mean;<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>        /**<a name="line.55"></a>
<FONT color="green">056</FONT>         * Maximum number of iterations for cumulative probability. Cumulative<a name="line.56"></a>
<FONT color="green">057</FONT>         * probabilities are estimated using either Lanczos series approximation<a name="line.57"></a>
<FONT color="green">058</FONT>         * of {@link Gamma#regularizedGammaP(double, double, double, int)}<a name="line.58"></a>
<FONT color="green">059</FONT>         * or continued fraction approximation of<a name="line.59"></a>
<FONT color="green">060</FONT>         * {@link Gamma#regularizedGammaQ(double, double, double, int)}.<a name="line.60"></a>
<FONT color="green">061</FONT>         */<a name="line.61"></a>
<FONT color="green">062</FONT>        private final int maxIterations;<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        /** Convergence criterion for cumulative probability. */<a name="line.64"></a>
<FONT color="green">065</FONT>        private final double epsilon;<a name="line.65"></a>
<FONT color="green">066</FONT>    <a name="line.66"></a>
<FONT color="green">067</FONT>        /**<a name="line.67"></a>
<FONT color="green">068</FONT>         * Creates a new Poisson distribution with specified mean.<a name="line.68"></a>
<FONT color="green">069</FONT>         *<a name="line.69"></a>
<FONT color="green">070</FONT>         * @param p the Poisson mean<a name="line.70"></a>
<FONT color="green">071</FONT>         * @throws NotStrictlyPositiveException if {@code p &lt;= 0}.<a name="line.71"></a>
<FONT color="green">072</FONT>         */<a name="line.72"></a>
<FONT color="green">073</FONT>        public PoissonDistribution(double p) throws NotStrictlyPositiveException {<a name="line.73"></a>
<FONT color="green">074</FONT>            this(p, DEFAULT_EPSILON, DEFAULT_MAX_ITERATIONS);<a name="line.74"></a>
<FONT color="green">075</FONT>        }<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>        /**<a name="line.77"></a>
<FONT color="green">078</FONT>         * Creates a new Poisson distribution with specified mean, convergence<a name="line.78"></a>
<FONT color="green">079</FONT>         * criterion and maximum number of iterations.<a name="line.79"></a>
<FONT color="green">080</FONT>         *<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param p Poisson mean.<a name="line.81"></a>
<FONT color="green">082</FONT>         * @param epsilon Convergence criterion for cumulative probabilities.<a name="line.82"></a>
<FONT color="green">083</FONT>         * @param maxIterations the maximum number of iterations for cumulative<a name="line.83"></a>
<FONT color="green">084</FONT>         * probabilities.<a name="line.84"></a>
<FONT color="green">085</FONT>         * @throws NotStrictlyPositiveException if {@code p &lt;= 0}.<a name="line.85"></a>
<FONT color="green">086</FONT>         * @since 2.1<a name="line.86"></a>
<FONT color="green">087</FONT>         */<a name="line.87"></a>
<FONT color="green">088</FONT>        public PoissonDistribution(double p, double epsilon, int maxIterations)<a name="line.88"></a>
<FONT color="green">089</FONT>        throws NotStrictlyPositiveException {<a name="line.89"></a>
<FONT color="green">090</FONT>            this(new Well19937c(), p, epsilon, maxIterations);<a name="line.90"></a>
<FONT color="green">091</FONT>        }<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>        /**<a name="line.93"></a>
<FONT color="green">094</FONT>         * Creates a new Poisson distribution with specified mean, convergence<a name="line.94"></a>
<FONT color="green">095</FONT>         * criterion and maximum number of iterations.<a name="line.95"></a>
<FONT color="green">096</FONT>         *<a name="line.96"></a>
<FONT color="green">097</FONT>         * @param rng Random number generator.<a name="line.97"></a>
<FONT color="green">098</FONT>         * @param p Poisson mean.<a name="line.98"></a>
<FONT color="green">099</FONT>         * @param epsilon Convergence criterion for cumulative probabilities.<a name="line.99"></a>
<FONT color="green">100</FONT>         * @param maxIterations the maximum number of iterations for cumulative<a name="line.100"></a>
<FONT color="green">101</FONT>         * probabilities.<a name="line.101"></a>
<FONT color="green">102</FONT>         * @throws NotStrictlyPositiveException if {@code p &lt;= 0}.<a name="line.102"></a>
<FONT color="green">103</FONT>         * @since 3.1<a name="line.103"></a>
<FONT color="green">104</FONT>         */<a name="line.104"></a>
<FONT color="green">105</FONT>        public PoissonDistribution(RandomGenerator rng,<a name="line.105"></a>
<FONT color="green">106</FONT>                                   double p,<a name="line.106"></a>
<FONT color="green">107</FONT>                                   double epsilon,<a name="line.107"></a>
<FONT color="green">108</FONT>                                   int maxIterations)<a name="line.108"></a>
<FONT color="green">109</FONT>        throws NotStrictlyPositiveException {<a name="line.109"></a>
<FONT color="green">110</FONT>            super(rng);<a name="line.110"></a>
<FONT color="green">111</FONT>    <a name="line.111"></a>
<FONT color="green">112</FONT>            if (p &lt;= 0) {<a name="line.112"></a>
<FONT color="green">113</FONT>                throw new NotStrictlyPositiveException(LocalizedFormats.MEAN, p);<a name="line.113"></a>
<FONT color="green">114</FONT>            }<a name="line.114"></a>
<FONT color="green">115</FONT>            mean = p;<a name="line.115"></a>
<FONT color="green">116</FONT>            this.epsilon = epsilon;<a name="line.116"></a>
<FONT color="green">117</FONT>            this.maxIterations = maxIterations;<a name="line.117"></a>
<FONT color="green">118</FONT>    <a name="line.118"></a>
<FONT color="green">119</FONT>            // Use the same RNG instance as the parent class.<a name="line.119"></a>
<FONT color="green">120</FONT>            normal = new NormalDistribution(rng, p, FastMath.sqrt(p),<a name="line.120"></a>
<FONT color="green">121</FONT>                                            NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);<a name="line.121"></a>
<FONT color="green">122</FONT>            exponential = new ExponentialDistribution(rng, 1,<a name="line.122"></a>
<FONT color="green">123</FONT>                                                      ExponentialDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);<a name="line.123"></a>
<FONT color="green">124</FONT>        }<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        /**<a name="line.126"></a>
<FONT color="green">127</FONT>         * Creates a new Poisson distribution with the specified mean and<a name="line.127"></a>
<FONT color="green">128</FONT>         * convergence criterion.<a name="line.128"></a>
<FONT color="green">129</FONT>         *<a name="line.129"></a>
<FONT color="green">130</FONT>         * @param p Poisson mean.<a name="line.130"></a>
<FONT color="green">131</FONT>         * @param epsilon Convergence criterion for cumulative probabilities.<a name="line.131"></a>
<FONT color="green">132</FONT>         * @throws NotStrictlyPositiveException if {@code p &lt;= 0}.<a name="line.132"></a>
<FONT color="green">133</FONT>         * @since 2.1<a name="line.133"></a>
<FONT color="green">134</FONT>         */<a name="line.134"></a>
<FONT color="green">135</FONT>        public PoissonDistribution(double p, double epsilon)<a name="line.135"></a>
<FONT color="green">136</FONT>        throws NotStrictlyPositiveException {<a name="line.136"></a>
<FONT color="green">137</FONT>            this(p, epsilon, DEFAULT_MAX_ITERATIONS);<a name="line.137"></a>
<FONT color="green">138</FONT>        }<a name="line.138"></a>
<FONT color="green">139</FONT>    <a name="line.139"></a>
<FONT color="green">140</FONT>        /**<a name="line.140"></a>
<FONT color="green">141</FONT>         * Creates a new Poisson distribution with the specified mean and maximum<a name="line.141"></a>
<FONT color="green">142</FONT>         * number of iterations.<a name="line.142"></a>
<FONT color="green">143</FONT>         *<a name="line.143"></a>
<FONT color="green">144</FONT>         * @param p Poisson mean.<a name="line.144"></a>
<FONT color="green">145</FONT>         * @param maxIterations Maximum number of iterations for cumulative<a name="line.145"></a>
<FONT color="green">146</FONT>         * probabilities.<a name="line.146"></a>
<FONT color="green">147</FONT>         * @since 2.1<a name="line.147"></a>
<FONT color="green">148</FONT>         */<a name="line.148"></a>
<FONT color="green">149</FONT>        public PoissonDistribution(double p, int maxIterations) {<a name="line.149"></a>
<FONT color="green">150</FONT>            this(p, DEFAULT_EPSILON, maxIterations);<a name="line.150"></a>
<FONT color="green">151</FONT>        }<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>        /**<a name="line.153"></a>
<FONT color="green">154</FONT>         * Get the mean for the distribution.<a name="line.154"></a>
<FONT color="green">155</FONT>         *<a name="line.155"></a>
<FONT color="green">156</FONT>         * @return the mean for the distribution.<a name="line.156"></a>
<FONT color="green">157</FONT>         */<a name="line.157"></a>
<FONT color="green">158</FONT>        public double getMean() {<a name="line.158"></a>
<FONT color="green">159</FONT>            return mean;<a name="line.159"></a>
<FONT color="green">160</FONT>        }<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>        /** {@inheritDoc} */<a name="line.162"></a>
<FONT color="green">163</FONT>        public double probability(int x) {<a name="line.163"></a>
<FONT color="green">164</FONT>            double ret;<a name="line.164"></a>
<FONT color="green">165</FONT>            if (x &lt; 0 || x == Integer.MAX_VALUE) {<a name="line.165"></a>
<FONT color="green">166</FONT>                ret = 0.0;<a name="line.166"></a>
<FONT color="green">167</FONT>            } else if (x == 0) {<a name="line.167"></a>
<FONT color="green">168</FONT>                ret = FastMath.exp(-mean);<a name="line.168"></a>
<FONT color="green">169</FONT>            } else {<a name="line.169"></a>
<FONT color="green">170</FONT>                ret = FastMath.exp(-SaddlePointExpansion.getStirlingError(x) -<a name="line.170"></a>
<FONT color="green">171</FONT>                      SaddlePointExpansion.getDeviancePart(x, mean)) /<a name="line.171"></a>
<FONT color="green">172</FONT>                      FastMath.sqrt(MathUtils.TWO_PI * x);<a name="line.172"></a>
<FONT color="green">173</FONT>            }<a name="line.173"></a>
<FONT color="green">174</FONT>            return ret;<a name="line.174"></a>
<FONT color="green">175</FONT>        }<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>        /** {@inheritDoc} */<a name="line.177"></a>
<FONT color="green">178</FONT>        public double cumulativeProbability(int x) {<a name="line.178"></a>
<FONT color="green">179</FONT>            if (x &lt; 0) {<a name="line.179"></a>
<FONT color="green">180</FONT>                return 0;<a name="line.180"></a>
<FONT color="green">181</FONT>            }<a name="line.181"></a>
<FONT color="green">182</FONT>            if (x == Integer.MAX_VALUE) {<a name="line.182"></a>
<FONT color="green">183</FONT>                return 1;<a name="line.183"></a>
<FONT color="green">184</FONT>            }<a name="line.184"></a>
<FONT color="green">185</FONT>            return Gamma.regularizedGammaQ((double) x + 1, mean, epsilon,<a name="line.185"></a>
<FONT color="green">186</FONT>                                           maxIterations);<a name="line.186"></a>
<FONT color="green">187</FONT>        }<a name="line.187"></a>
<FONT color="green">188</FONT>    <a name="line.188"></a>
<FONT color="green">189</FONT>        /**<a name="line.189"></a>
<FONT color="green">190</FONT>         * Calculates the Poisson distribution function using a normal<a name="line.190"></a>
<FONT color="green">191</FONT>         * approximation. The {@code N(mean, sqrt(mean))} distribution is used<a name="line.191"></a>
<FONT color="green">192</FONT>         * to approximate the Poisson distribution. The computation uses<a name="line.192"></a>
<FONT color="green">193</FONT>         * "half-correction" (evaluating the normal distribution function at<a name="line.193"></a>
<FONT color="green">194</FONT>         * {@code x + 0.5}).<a name="line.194"></a>
<FONT color="green">195</FONT>         *<a name="line.195"></a>
<FONT color="green">196</FONT>         * @param x Upper bound, inclusive.<a name="line.196"></a>
<FONT color="green">197</FONT>         * @return the distribution function value calculated using a normal<a name="line.197"></a>
<FONT color="green">198</FONT>         * approximation.<a name="line.198"></a>
<FONT color="green">199</FONT>         */<a name="line.199"></a>
<FONT color="green">200</FONT>        public double normalApproximateProbability(int x)  {<a name="line.200"></a>
<FONT color="green">201</FONT>            // calculate the probability using half-correction<a name="line.201"></a>
<FONT color="green">202</FONT>            return normal.cumulativeProbability(x + 0.5);<a name="line.202"></a>
<FONT color="green">203</FONT>        }<a name="line.203"></a>
<FONT color="green">204</FONT>    <a name="line.204"></a>
<FONT color="green">205</FONT>        /**<a name="line.205"></a>
<FONT color="green">206</FONT>         * {@inheritDoc}<a name="line.206"></a>
<FONT color="green">207</FONT>         *<a name="line.207"></a>
<FONT color="green">208</FONT>         * For mean parameter {@code p}, the mean is {@code p}.<a name="line.208"></a>
<FONT color="green">209</FONT>         */<a name="line.209"></a>
<FONT color="green">210</FONT>        public double getNumericalMean() {<a name="line.210"></a>
<FONT color="green">211</FONT>            return getMean();<a name="line.211"></a>
<FONT color="green">212</FONT>        }<a name="line.212"></a>
<FONT color="green">213</FONT>    <a name="line.213"></a>
<FONT color="green">214</FONT>        /**<a name="line.214"></a>
<FONT color="green">215</FONT>         * {@inheritDoc}<a name="line.215"></a>
<FONT color="green">216</FONT>         *<a name="line.216"></a>
<FONT color="green">217</FONT>         * For mean parameter {@code p}, the variance is {@code p}.<a name="line.217"></a>
<FONT color="green">218</FONT>         */<a name="line.218"></a>
<FONT color="green">219</FONT>        public double getNumericalVariance() {<a name="line.219"></a>
<FONT color="green">220</FONT>            return getMean();<a name="line.220"></a>
<FONT color="green">221</FONT>        }<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>        /**<a name="line.223"></a>
<FONT color="green">224</FONT>         * {@inheritDoc}<a name="line.224"></a>
<FONT color="green">225</FONT>         *<a name="line.225"></a>
<FONT color="green">226</FONT>         * The lower bound of the support is always 0 no matter the mean parameter.<a name="line.226"></a>
<FONT color="green">227</FONT>         *<a name="line.227"></a>
<FONT color="green">228</FONT>         * @return lower bound of the support (always 0)<a name="line.228"></a>
<FONT color="green">229</FONT>         */<a name="line.229"></a>
<FONT color="green">230</FONT>        public int getSupportLowerBound() {<a name="line.230"></a>
<FONT color="green">231</FONT>            return 0;<a name="line.231"></a>
<FONT color="green">232</FONT>        }<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>        /**<a name="line.234"></a>
<FONT color="green">235</FONT>         * {@inheritDoc}<a name="line.235"></a>
<FONT color="green">236</FONT>         *<a name="line.236"></a>
<FONT color="green">237</FONT>         * The upper bound of the support is positive infinity,<a name="line.237"></a>
<FONT color="green">238</FONT>         * regardless of the parameter values. There is no integer infinity,<a name="line.238"></a>
<FONT color="green">239</FONT>         * so this method returns {@code Integer.MAX_VALUE}.<a name="line.239"></a>
<FONT color="green">240</FONT>         *<a name="line.240"></a>
<FONT color="green">241</FONT>         * @return upper bound of the support (always {@code Integer.MAX_VALUE} for<a name="line.241"></a>
<FONT color="green">242</FONT>         * positive infinity)<a name="line.242"></a>
<FONT color="green">243</FONT>         */<a name="line.243"></a>
<FONT color="green">244</FONT>        public int getSupportUpperBound() {<a name="line.244"></a>
<FONT color="green">245</FONT>            return Integer.MAX_VALUE;<a name="line.245"></a>
<FONT color="green">246</FONT>        }<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>        /**<a name="line.248"></a>
<FONT color="green">249</FONT>         * {@inheritDoc}<a name="line.249"></a>
<FONT color="green">250</FONT>         *<a name="line.250"></a>
<FONT color="green">251</FONT>         * The support of this distribution is connected.<a name="line.251"></a>
<FONT color="green">252</FONT>         *<a name="line.252"></a>
<FONT color="green">253</FONT>         * @return {@code true}<a name="line.253"></a>
<FONT color="green">254</FONT>         */<a name="line.254"></a>
<FONT color="green">255</FONT>        public boolean isSupportConnected() {<a name="line.255"></a>
<FONT color="green">256</FONT>            return true;<a name="line.256"></a>
<FONT color="green">257</FONT>        }<a name="line.257"></a>
<FONT color="green">258</FONT>    <a name="line.258"></a>
<FONT color="green">259</FONT>        /**<a name="line.259"></a>
<FONT color="green">260</FONT>         * {@inheritDoc}<a name="line.260"></a>
<FONT color="green">261</FONT>         * &lt;p&gt;<a name="line.261"></a>
<FONT color="green">262</FONT>         * &lt;strong&gt;Algorithm Description&lt;/strong&gt;:<a name="line.262"></a>
<FONT color="green">263</FONT>         * &lt;ul&gt;<a name="line.263"></a>
<FONT color="green">264</FONT>         *  &lt;li&gt;For small means, uses simulation of a Poisson process<a name="line.264"></a>
<FONT color="green">265</FONT>         *   using Uniform deviates, as described<a name="line.265"></a>
<FONT color="green">266</FONT>         *   &lt;a href="http://irmi.epfl.ch/cmos/Pmmi/interactive/rng7.htm"&gt; here&lt;/a&gt;.<a name="line.266"></a>
<FONT color="green">267</FONT>         *   The Poisson process (and hence value returned) is bounded by 1000 * mean.<a name="line.267"></a>
<FONT color="green">268</FONT>         *  &lt;/li&gt;<a name="line.268"></a>
<FONT color="green">269</FONT>         *  &lt;li&gt;For large means, uses the rejection algorithm described in<a name="line.269"></a>
<FONT color="green">270</FONT>         *   &lt;quote&gt;<a name="line.270"></a>
<FONT color="green">271</FONT>         *    Devroye, Luc. (1981).&lt;i&gt;The Computer Generation of Poisson Random Variables&lt;/i&gt;<a name="line.271"></a>
<FONT color="green">272</FONT>         *    &lt;strong&gt;Computing&lt;/strong&gt; vol. 26 pp. 197-207.<a name="line.272"></a>
<FONT color="green">273</FONT>         *   &lt;/quote&gt;<a name="line.273"></a>
<FONT color="green">274</FONT>         *  &lt;/li&gt;<a name="line.274"></a>
<FONT color="green">275</FONT>         * &lt;/ul&gt;<a name="line.275"></a>
<FONT color="green">276</FONT>         * &lt;/p&gt;<a name="line.276"></a>
<FONT color="green">277</FONT>         *<a name="line.277"></a>
<FONT color="green">278</FONT>         * @return a random value.<a name="line.278"></a>
<FONT color="green">279</FONT>         * @since 2.2<a name="line.279"></a>
<FONT color="green">280</FONT>         */<a name="line.280"></a>
<FONT color="green">281</FONT>        @Override<a name="line.281"></a>
<FONT color="green">282</FONT>        public int sample() {<a name="line.282"></a>
<FONT color="green">283</FONT>            return (int) FastMath.min(nextPoisson(mean), Integer.MAX_VALUE);<a name="line.283"></a>
<FONT color="green">284</FONT>        }<a name="line.284"></a>
<FONT color="green">285</FONT>    <a name="line.285"></a>
<FONT color="green">286</FONT>        /**<a name="line.286"></a>
<FONT color="green">287</FONT>         * @param meanPoisson Mean of the Poisson distribution.<a name="line.287"></a>
<FONT color="green">288</FONT>         * @return the next sample.<a name="line.288"></a>
<FONT color="green">289</FONT>         */<a name="line.289"></a>
<FONT color="green">290</FONT>        private long nextPoisson(double meanPoisson) {<a name="line.290"></a>
<FONT color="green">291</FONT>            final double pivot = 40.0d;<a name="line.291"></a>
<FONT color="green">292</FONT>            if (meanPoisson &lt; pivot) {<a name="line.292"></a>
<FONT color="green">293</FONT>                double p = FastMath.exp(-meanPoisson);<a name="line.293"></a>
<FONT color="green">294</FONT>                long n = 0;<a name="line.294"></a>
<FONT color="green">295</FONT>                double r = 1.0d;<a name="line.295"></a>
<FONT color="green">296</FONT>                double rnd = 1.0d;<a name="line.296"></a>
<FONT color="green">297</FONT>    <a name="line.297"></a>
<FONT color="green">298</FONT>                while (n &lt; 1000 * meanPoisson) {<a name="line.298"></a>
<FONT color="green">299</FONT>                    rnd = random.nextDouble();<a name="line.299"></a>
<FONT color="green">300</FONT>                    r = r * rnd;<a name="line.300"></a>
<FONT color="green">301</FONT>                    if (r &gt;= p) {<a name="line.301"></a>
<FONT color="green">302</FONT>                        n++;<a name="line.302"></a>
<FONT color="green">303</FONT>                    } else {<a name="line.303"></a>
<FONT color="green">304</FONT>                        return n;<a name="line.304"></a>
<FONT color="green">305</FONT>                    }<a name="line.305"></a>
<FONT color="green">306</FONT>                }<a name="line.306"></a>
<FONT color="green">307</FONT>                return n;<a name="line.307"></a>
<FONT color="green">308</FONT>            } else {<a name="line.308"></a>
<FONT color="green">309</FONT>                final double lambda = FastMath.floor(meanPoisson);<a name="line.309"></a>
<FONT color="green">310</FONT>                final double lambdaFractional = meanPoisson - lambda;<a name="line.310"></a>
<FONT color="green">311</FONT>                final double logLambda = FastMath.log(lambda);<a name="line.311"></a>
<FONT color="green">312</FONT>                final double logLambdaFactorial = ArithmeticUtils.factorialLog((int) lambda);<a name="line.312"></a>
<FONT color="green">313</FONT>                final long y2 = lambdaFractional &lt; Double.MIN_VALUE ? 0 : nextPoisson(lambdaFractional);<a name="line.313"></a>
<FONT color="green">314</FONT>                final double delta = FastMath.sqrt(lambda * FastMath.log(32 * lambda / FastMath.PI + 1));<a name="line.314"></a>
<FONT color="green">315</FONT>                final double halfDelta = delta / 2;<a name="line.315"></a>
<FONT color="green">316</FONT>                final double twolpd = 2 * lambda + delta;<a name="line.316"></a>
<FONT color="green">317</FONT>                final double a1 = FastMath.sqrt(FastMath.PI * twolpd) * FastMath.exp(1 / 8 * lambda);<a name="line.317"></a>
<FONT color="green">318</FONT>                final double a2 = (twolpd / delta) * FastMath.exp(-delta * (1 + delta) / twolpd);<a name="line.318"></a>
<FONT color="green">319</FONT>                final double aSum = a1 + a2 + 1;<a name="line.319"></a>
<FONT color="green">320</FONT>                final double p1 = a1 / aSum;<a name="line.320"></a>
<FONT color="green">321</FONT>                final double p2 = a2 / aSum;<a name="line.321"></a>
<FONT color="green">322</FONT>                final double c1 = 1 / (8 * lambda);<a name="line.322"></a>
<FONT color="green">323</FONT>    <a name="line.323"></a>
<FONT color="green">324</FONT>                double x = 0;<a name="line.324"></a>
<FONT color="green">325</FONT>                double y = 0;<a name="line.325"></a>
<FONT color="green">326</FONT>                double v = 0;<a name="line.326"></a>
<FONT color="green">327</FONT>                int a = 0;<a name="line.327"></a>
<FONT color="green">328</FONT>                double t = 0;<a name="line.328"></a>
<FONT color="green">329</FONT>                double qr = 0;<a name="line.329"></a>
<FONT color="green">330</FONT>                double qa = 0;<a name="line.330"></a>
<FONT color="green">331</FONT>                for (;;) {<a name="line.331"></a>
<FONT color="green">332</FONT>                    final double u = random.nextDouble();<a name="line.332"></a>
<FONT color="green">333</FONT>                    if (u &lt;= p1) {<a name="line.333"></a>
<FONT color="green">334</FONT>                        final double n = random.nextGaussian();<a name="line.334"></a>
<FONT color="green">335</FONT>                        x = n * FastMath.sqrt(lambda + halfDelta) - 0.5d;<a name="line.335"></a>
<FONT color="green">336</FONT>                        if (x &gt; delta || x &lt; -lambda) {<a name="line.336"></a>
<FONT color="green">337</FONT>                            continue;<a name="line.337"></a>
<FONT color="green">338</FONT>                        }<a name="line.338"></a>
<FONT color="green">339</FONT>                        y = x &lt; 0 ? FastMath.floor(x) : FastMath.ceil(x);<a name="line.339"></a>
<FONT color="green">340</FONT>                        final double e = exponential.sample();<a name="line.340"></a>
<FONT color="green">341</FONT>                        v = -e - (n * n / 2) + c1;<a name="line.341"></a>
<FONT color="green">342</FONT>                    } else {<a name="line.342"></a>
<FONT color="green">343</FONT>                        if (u &gt; p1 + p2) {<a name="line.343"></a>
<FONT color="green">344</FONT>                            y = lambda;<a name="line.344"></a>
<FONT color="green">345</FONT>                            break;<a name="line.345"></a>
<FONT color="green">346</FONT>                        } else {<a name="line.346"></a>
<FONT color="green">347</FONT>                            x = delta + (twolpd / delta) * exponential.sample();<a name="line.347"></a>
<FONT color="green">348</FONT>                            y = FastMath.ceil(x);<a name="line.348"></a>
<FONT color="green">349</FONT>                            v = -exponential.sample() - delta * (x + 1) / twolpd;<a name="line.349"></a>
<FONT color="green">350</FONT>                        }<a name="line.350"></a>
<FONT color="green">351</FONT>                    }<a name="line.351"></a>
<FONT color="green">352</FONT>                    a = x &lt; 0 ? 1 : 0;<a name="line.352"></a>
<FONT color="green">353</FONT>                    t = y * (y + 1) / (2 * lambda);<a name="line.353"></a>
<FONT color="green">354</FONT>                    if (v &lt; -t &amp;&amp; a == 0) {<a name="line.354"></a>
<FONT color="green">355</FONT>                        y = lambda + y;<a name="line.355"></a>
<FONT color="green">356</FONT>                        break;<a name="line.356"></a>
<FONT color="green">357</FONT>                    }<a name="line.357"></a>
<FONT color="green">358</FONT>                    qr = t * ((2 * y + 1) / (6 * lambda) - 1);<a name="line.358"></a>
<FONT color="green">359</FONT>                    qa = qr - (t * t) / (3 * (lambda + a * (y + 1)));<a name="line.359"></a>
<FONT color="green">360</FONT>                    if (v &lt; qa) {<a name="line.360"></a>
<FONT color="green">361</FONT>                        y = lambda + y;<a name="line.361"></a>
<FONT color="green">362</FONT>                        break;<a name="line.362"></a>
<FONT color="green">363</FONT>                    }<a name="line.363"></a>
<FONT color="green">364</FONT>                    if (v &gt; qr) {<a name="line.364"></a>
<FONT color="green">365</FONT>                        continue;<a name="line.365"></a>
<FONT color="green">366</FONT>                    }<a name="line.366"></a>
<FONT color="green">367</FONT>                    if (v &lt; y * logLambda - ArithmeticUtils.factorialLog((int) (y + lambda)) + logLambdaFactorial) {<a name="line.367"></a>
<FONT color="green">368</FONT>                        y = lambda + y;<a name="line.368"></a>
<FONT color="green">369</FONT>                        break;<a name="line.369"></a>
<FONT color="green">370</FONT>                    }<a name="line.370"></a>
<FONT color="green">371</FONT>                }<a name="line.371"></a>
<FONT color="green">372</FONT>                return y2 + (long) y;<a name="line.372"></a>
<FONT color="green">373</FONT>            }<a name="line.373"></a>
<FONT color="green">374</FONT>        }<a name="line.374"></a>
<FONT color="green">375</FONT>    }<a name="line.375"></a>




























































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